If you get a few moments, can you tell us what characteristics you used for your ID. I looked in Sibley's and also in Wheeler's Raptors of Western North America and I just don't know how to tell the difference.
If I could see a Cooper's juvi next to a Sharpie juvi, I think I could tell, but it is hard to know if the bottom white stripe on the tail is wide or narrow or if the legs are thin or not with nothing to compare to.
Other things I looked at ...
Size of head - same problem - no reference
Size of bird - I guess a small bird (11 to 15") would be likely a Sharpie and probably male and a really large one (greater than 23") would likely be a Cooper's and maybe female. But, my guess would be this bird is around 22" if the fencepost that the feeder hanger is on is about 4 inches wide. So, that could be either one.
Short tail or long tail - I can't tell.
Squared tail or rounded tail - Does look somewhat rounded to me which would indicate Cooper's.
Streaks - coarse, brown for Sharpie and Thin, dark for Cooper's. I can't tell.
Is there anything else that I am missing?
Any help in how to decide would be most appreciated.
I wonder if a mod could move this to the Bird ID forum. I think there are other newbies like me that could benefit from this discussion. I will see if I can figure out how to send in a request to move it.